§6.1–2 Magnetization Christopher Crawford PHY

HW 10 hints 2

Outline Multipoles – reviewcompare: Q E – Internal, external Magnetic Dipole m=I Acompare: p=q d – Dynamics – torque, potential, forcecompare: E – Diamagnetismcompare: α – Paramagnetismcompare: α Magnetization Density M=dm/dτcompare: P – Magnetization sheets– flow – Magnetization solenoids– fluxcompare: Φ P – Magnetization currents J b, K b compare: ρ b, σ b Boundary value problem – Dipole sphere with surface current K b compare: σ b 3

Multipoles – review Electric multipoles – No external monopole – just a constant potential offset Magnetic multipoles – Derivatives P’(x) –> there is NO monopole at all 4

Magnetic dipole Electric dipole – Remember pure spherical surface charge dipole – Torque – Potential Magnetic dipole – Gilbert vs Ampere dipole – We will solve same BVP: spherical surface current dipole today – Torque – Potential 5

Electric vs. magnetic dipole force Electric dipole Magnetic dipole 6

Diamagnetism Induced electric polarizability α e of all molecules Diamagnetism – Dipoles oriented opposite to field! – Compare direction of E b, B b 7 Wikipedia: Magnetic_levitation A live frog levitates inside a 32 mm diameter vertical bore of a Bitter solenoid in a magnetic field of about 16 Teslas

Paramagnetism Electric polarizability α e of permanent dipoles Paramagnetism – Exhibited in all atoms, stronger than diagmagnetism – often cancelled out by Pauli exclusion principle 8

Magnetization density Polarization density – Polarization chains– flux – Bound charge Magnetization density – Magnetization mesh– flow – Magnetization solenoids– flux – Bound currents 9

Calculation of bound potential 10

Boundary value problem #1 11

Boundary value problem #2 12